Blow-up solutions to a system of nonlinear Volterra equations

A system of nonlinear Volterra integral equations with convolution kernels is considered. Estimates are given for the blow-up time when conditions are such that the solution is known to become unbounded in finite time. For two examples that arise in combustion problems, numerical estimates of blow-u...

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Bibliographic Details
Published in:Journal of mathematical analysis and applications 2005, Vol.301 (1), p.208-218
Main Authors: Mydlarczyk, W., Okrasiński, W., Roberts, C.A.
Format: Article
Language:English
Subjects:
Asymptotic behavior
Blow-up time
Exact sciences and technology
Explosion
Integral equations
Mathematical analysis
Mathematics
Sciences and techniques of general use
System of integral equations
Volterra
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Summary:A system of nonlinear Volterra integral equations with convolution kernels is considered. Estimates are given for the blow-up time when conditions are such that the solution is known to become unbounded in finite time. For two examples that arise in combustion problems, numerical estimates of blow-up time are presented. Additionally, the asymptotic behavior of the blow-up solution in the key limit is established for the power-law and exponential nonlinearity cases.
ISSN:0022-247X
1096-0813
DOI:10.1016/j.jmaa.2004.07.014